According to its state website, Tennessee has a long execution history, with hanging and the electric chair as two prior methods -- electrocution still being a viable alternative that has been used as late as 2007:

Until 1913, all individuals convicted of a capital offense were hanged. There are no official records of the number or names of those executed. From 1913 to 1915, there was no capital punishment in Tennessee. C. Rye was Governor during the first execution by electrocution. From 1916 until 1960, 125 persons were executed by electrocution in Tennessee. In 2000, lethal injection replaced electrocution as the primary method of execution. In September, 2007 the first electrocution in 47 years was carried out.

Oklahoma has decided upon pentobarbital.

Of course, there's already a precedent set for using pentobarbital that Tennessee could follow. Oklahoma already treated John David Duty, Billy Don Alverson, and Jeffrey David Matthews just like veterarians treat dogs and cats all over the country, when they used pentobarbital in their executions. And apparently, Oklahoma is fine with this and plans to continue using pentobarbital, according to its website description of its execution methods.